I don’t think I’ll dive deeper than quoting Wikipedia:

Most fixed-size integer formats cannot explicitly indicate invalid data. In such a case, when converting NaN to an integer type, the IEEE 754 standard requires that the invalid-operation exception be signaled.

For example in Java, such operations throw instances of java.lang.ArithmeticException.

In C, they lead to undefined behavior, but if annex F is supported, the operation yields an "invalid" floating-point exception (as required by the IEEE standard) and an unspecified value.

In the R language, the minimal signed value (i.e. 0x80000000) of integers is reserved for NA (Not available).[citation needed] Conversions from NaN (or double NA) to integers then yield a NA integer.

Perl's Math::BigInt package uses "NaN" for the result of strings that do not represent valid integers.